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Sib. Zh. Ind. Mat., 2014, Volume 17, Number 1, Pages 135–148 (Mi sjim826)  

This article is cited in 3 scientific papers (total in 3 papers)

On the solvability of special systems of one-dimensional loaded parabolic equations and composite-type systems with Cauchy data

I. V. Frolenkov, G. V. Romanenko

Siberian Federal University, 79 Svobodny av., 660041 Krasnoyarsk

Abstract: We study a one-dimensional system of two parabolic loaded equations of special kind and one-dimensional composite-type systems of special kind. Both systems are considered with Cauchy data. We obtain sufficient conditions for the existence of solutions in the class of smooth bounded functions. The method of splitting on the differential level (the weak approximation method) is used in the proof.

Keywords: inverse problem, direct problem, loaded equation, parabolic equation, weak approximation method, system of partial differential equations, composite-type system.

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English version:
Journal of Applied and Industrial Mathematics, 2014, 8:2, 196–207

Bibliographic databases:

UDC: 517.9
Received: 10.10.2013

Citation: I. V. Frolenkov, G. V. Romanenko, “On the solvability of special systems of one-dimensional loaded parabolic equations and composite-type systems with Cauchy data”, Sib. Zh. Ind. Mat., 17:1 (2014), 135–148; J. Appl. Industr. Math., 8:2 (2014), 196–207

Citation in format AMSBIB
\Bibitem{FroRom14}
\by I.~V.~Frolenkov, G.~V.~Romanenko
\paper On the solvability of special systems of one-dimensional loaded parabolic equations and composite-type systems with Cauchy data
\jour Sib. Zh. Ind. Mat.
\yr 2014
\vol 17
\issue 1
\pages 135--148
\mathnet{http://mi.mathnet.ru/sjim826}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3379261}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 2
\pages 196--207
\crossref{https://doi.org/10.1134/S1990478914020069}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. V. Romanenko, I. V. Frolenkov, “On the solvability of a system of two multidimensional loaded parabolic equations with the Cauchy data”, J. Sib. Fed. Univ.-Math. Phys., 9:3 (2016), 364–373  crossref  isi
    2. I. V. Frolenkov, E. N. Kriger, “O razreshimosti zadachi Koshi dlya odnogo klassa mnogomernykh nagruzhennykh parabolicheskikh uravnenii”, Matematicheskii analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 156, VINITI RAN, M., 2018, 41–57  mathnet
    3. I. V. Frolenkov, I. S. Antipina, N. M. Terskikh, “On Uniqueness and Continuous Dependence on the Initial Data of the Solution of a System of Two Loaded Parabolic Equations With the Cauchy Data”, Zhurn. SFU. Ser. Matem. i fiz., 12:3 (2019), 298–309  mathnet  crossref  mathscinet  isi  scopus
  • Сибирский журнал индустриальной математики
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